Question

An investment is expected to produce cash flows of $1,000 at the end of each of the next 6 years, then an additional lump sum payment of $1,500 at the end of Year 6. What is the maximum price you are willing to pay for this investment now if your expected rate of return is 4%?

Select one:

a. $5,324.89

b. $5,974.77

c. $5,568.13

d. $6,427.61

e. $4,854.13

Answer 1

Option (d) is correct

Price of the investment can be calculated by the following formula:

Price of the investment = Present value of cash flows of $1000 for 6 years + Present value of lump sum payment of $1500 at the end of 6 years

Cash flows will be same every year, so it is an annuity. Lump sum payment is a one time payment.

Now,

First we will calculate the Present value of cash flows of $1000 for 6 years:

For calculating the present value, we will use the following formula:

PVA = P * (1 - (1 + r)^-n / r)

where, PVA = Present value of annuity, P is the periodical amount = $1000, r is the rate of interest = 4% and n is the time period = 6

Now, putting these values in the above formula, we get,

PVA = $1000 * (1 - (1 + 4%)^-6 / 4%)

PVA = $1000 * (1 - ( 1+ 0.04)^-6 / 0.04)

PVA = $1000 * (1 - ( 1.04)^-6 / 0.04)

PVA = $1000 * ((1 - 0.79031452573) / 0.04)

PVA = $1000 * (0.20968547427 / 0.04)

PVA = $1000 * 5.24213685675

PVA = $5242.14

Next, we will calculate the present value of lump sum payment:

For calculating present value, we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value = $1500, PV = Present value, r = rate of interest = 4%, n= time period = 6

now, putting theses values in the above equation, we get,

$1500 = PV * (1 + 4%)⁶

$1500 = PV * (1 + 0.04)⁶

$1500 = PV * (1.04)⁶

$1500 = PV * 1.2653190185

PV = $1500 / 1.2653190185

PV = $1185.47

Now,

Price of the investment = Present value of cash flows of $1000 for 6 years + Present value of lump sum payment of $1500 at the end of 6 years.

Price of the investment = $5242.14 + $1185.47 = $6427.61